As far as I know, a layer can be Clipped only by Clipping using all the features of another layer. If I want to clip using only a particular feature within a layer, it is necessary to first select that feature, then export it to a new feature class, and finally use this new feature class to clip the original layer.
You then have to repeat this process for each desired feature. It would be very handy if the clip command had something like "clip using selected feature".